Renormalization group improvement of the effective potential: an EFT approach

Manohar, Aneesh V.; Nardoni, Emily

doi:10.1007/jhep04(2021)093

Renormalization group improvement of the effective potential: an EFT approach

Journal Article · Mon Apr 12 00:00:00 EDT 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep04(2021)093· OSTI ID:1851205

Manohar, Aneesh V. ^[1]; Nardoni, Emily ^[2]

Univ. of California, San Diego, CA (United States). Dept. of Physics; Univ. of California, San Diego, CA (United States)
Univ. of California, Los Angeles, CA (United States). Dept. of Physics and Astronomy. Mani L. Bhaumik Inst. for Theoretical Physics

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Los Angeles, CA (United States); Univ. of California, San Diego, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009919; SC0020421

OSTI ID:: 1851205

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 4 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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71 CLASSICAL AND QUANTUM MECHANICS
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Renormalization group improvement of the effective potential: an EFT approach

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